%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:40:03 PM UTC 2026
% Result : Theorem 5.93s 2.12s
% Output : Refutation 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 13 unt; 1 def)
% Number of atoms : 94 ( 39 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 87 ( 35 ~; 31 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f44,axiom,
! [X0] :
( member(X0,universal_class)
=> member(member_of(singleton(X0)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_universal) ).
fof(f45,axiom,
! [X0] :
( member(X0,universal_class)
=> singleton(member_of(singleton(X0))) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_singleton) ).
fof(f48,conjecture,
! [X0,X1] :
( ( member(X1,universal_class)
& X0 = singleton(X1) )
=> member_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,universal_class)
& X0 = singleton(X1) )
=> member_of(X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f64,plain,
! [X0] :
( member(member_of(singleton(X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f44]) ).
fof(f65,plain,
! [X0] :
( singleton(member_of(singleton(X0))) = singleton(X0)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f66,plain,
? [X0,X1] :
( member_of(X0) != X1
& member(X1,universal_class)
& X0 = singleton(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f67,plain,
? [X0,X1] :
( member_of(X0) != X1
& member(X1,universal_class)
& X0 = singleton(X1) ),
inference(flattening,[],[f66]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f73]) ).
fof(f110,plain,
( sK7 != member_of(sK6)
& member(sK7,universal_class)
& sK6 = singleton(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f67]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f198,plain,
! [X0] :
( member(member_of(singleton(X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f64]) ).
fof(f199,plain,
! [X0] :
( singleton(X0) = singleton(member_of(singleton(X0)))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f65]) ).
fof(f202,plain,
sK6 = singleton(sK7),
inference(cnf_transformation,[],[f110]) ).
fof(f203,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f110]) ).
fof(f204,plain,
sK7 != member_of(sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f207,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f121]) ).
fof(f224,plain,
( member(member_of(sK6),universal_class)
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f198,f202]) ).
fof(f225,plain,
member(member_of(sK6),universal_class),
inference(forward_subsumption_resolution,[],[f224,f203]) ).
fof(f226,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f207,f123]) ).
fof(f320,definition,
( spl8_10
<=> sK6 = singleton(member_of(sK6)) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f322,plain,
( sK6 = singleton(member_of(sK6))
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f420,plain,
( sK6 = singleton(member_of(sK6))
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f199,f202]) ).
fof(f430,plain,
sK6 = singleton(member_of(sK6)),
inference(forward_subsumption_resolution,[],[f420,f203]) ).
fof(f431,plain,
spl8_10,
inference(avatar_split_clause,[],[f430,f320]) ).
fof(f447,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f118,f123]) ).
fof(f448,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f447]) ).
fof(f452,plain,
( member(member_of(sK6),sK6)
| ~ member(member_of(sK6),universal_class)
| ~ spl8_10 ),
inference(superposition,[],[f226,f322]) ).
fof(f456,plain,
( member(member_of(sK6),sK6)
| ~ spl8_10 ),
inference(forward_subsumption_resolution,[],[f452,f225]) ).
fof(f677,plain,
! [X0] :
( ~ member(X0,sK6)
| sK7 = X0 ),
inference(superposition,[],[f448,f202]) ).
fof(f682,plain,
( sK7 = member_of(sK6)
| ~ spl8_10 ),
inference(resolution,[],[f677,f456]) ).
fof(f701,plain,
( $false
| ~ spl8_10 ),
inference(forward_subsumption_resolution,[],[f682,f204]) ).
fof(f702,plain,
~ spl8_10,
inference(avatar_contradiction_clause,[],[f701]) ).
cnf(s13,plain,
spl8_10,
inference(sat_conversion,[],[f431]) ).
cnf(s29,plain,
~ spl8_10,
inference(sat_conversion,[],[f702]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s13,s29]) ).
fof(f708,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n006.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 28 00:37:41 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.52 Running first-order theorem proving
% 0.18/0.52 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.93/2.12 % (3484729)Detected formulas, will run a generic FOF schedule.
% 5.93/2.12 % (3484736)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2208334484:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.93/2.12 % (3484740)dis-21_1_sil=8000:lcm=predicate:random_seed=1446377513:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.93/2.12 % (3484735)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3601976020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.93/2.12 % (3484734)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4068118825:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.93/2.12 % (3484738)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=435521967:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.93/2.12 % (3484739)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=579411850:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.93/2.12 % (3484737)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1776041871:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.93/2.12 % (3484737)Refutation not found, incomplete strategy
% 5.93/2.12 % (3484737)------------------------------
% 5.93/2.12 % (3484737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484737)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484737)Termination reason: Refutation not found, incomplete strategy
% 5.93/2.12 % (3484737)Time elapsed: 0.002 s
% 5.93/2.12 % (3484737)Peak memory usage: 88 MB
% 5.93/2.12 % (3484738)Refutation not found, incomplete strategy
% 5.93/2.12 % (3484738)------------------------------
% 5.93/2.12 % (3484738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484738)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484738)Termination reason: Refutation not found, incomplete strategy
% 5.93/2.12 % (3484738)Time elapsed: 0.002 s
% 5.93/2.12 % (3484738)Peak memory usage: 87 MB
% 5.93/2.12 % (3484738)Instructions burned: 1 (million)
% 5.93/2.12 % (3484739)First to succeed.
% 5.93/2.12 % (3484739)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3484729"
% 5.93/2.12 % (3484740)Instruction limit reached!
% 5.93/2.12 % (3484740)------------------------------
% 5.93/2.12 % (3484740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484740)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484740)Termination reason: Instruction limit
% 5.93/2.12 % (3484740)Termination phase: Saturation
% 5.93/2.12 % (3484740)Time elapsed: 0.131 s
% 5.93/2.12 % (3484740)Peak memory usage: 90 MB
% 5.93/2.12 % (3484740)Instructions burned: 130 (million)
% 5.93/2.12 % (3484748)lrs+10_1_sil=8000:sp=occurrence:random_seed=2664610798:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.93/2.12 % (3484748)Instruction limit reached!
% 5.93/2.12 % (3484748)------------------------------
% 5.93/2.12 % (3484748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484748)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484748)Termination reason: Instruction limit
% 5.93/2.12 % (3484748)Termination phase: Saturation
% 5.93/2.12 % (3484748)Time elapsed: 0.135 s
% 5.93/2.12 % (3484748)Peak memory usage: 88 MB
% 5.93/2.12 % (3484748)Instructions burned: 288 (million)
% 5.93/2.12 % (3484737)------------------------------
% 5.93/2.12 % (3484737)------------------------------
% 5.93/2.12 % (3484738)------------------------------
% 5.93/2.12 % (3484738)------------------------------
% 5.93/2.12 % (3484736)Refutation not found, incomplete strategy
% 5.93/2.12 % (3484736)------------------------------
% 5.93/2.12 % (3484736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484736)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484736)Termination reason: Refutation not found, incomplete strategy
% 5.93/2.12 % (3484736)Time elapsed: 0.506 s
% 5.93/2.12 % (3484736)Peak memory usage: 128 MB
% 5.93/2.12 % (3484736)Instructions burned: 897 (million)
% 5.93/2.12 % (3484739)Refutation found. Thanks to Tanya!
% 5.93/2.12 % SZS status Theorem for theBenchmark
% 5.93/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 5.93/2.12 % (3484739)------------------------------
% 5.93/2.12 % (3484739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/2.12 % (3484739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/2.12 % (3484739)CaDiCaL version: 2.1.3
% 5.93/2.12 % (3484739)Termination reason: Refutation
% 5.93/2.12 % (3484739)Time elapsed: 0.032 s
% 5.93/2.12 % (3484739)Peak memory usage: 90 MB
% 5.93/2.12 % (3484739)Instructions burned: 24 (million)
% 5.93/2.12 % (3484739)------------------------------
% 5.93/2.12 % (3484739)------------------------------
% 5.93/2.12 % (3484729)Success in time 0.704 s
% 5.93/2.12 % Vampire exiting
%------------------------------------------------------------------------------